thekvs/gist:476bdd857d89a05098b8

## gistfile1.ipynb
{
 "metadata": {
  "name": "sympy-test-2"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from __future__ import division\nfrom sympy import *\nfrom sympy import init_printing\ninit_printing()\n\nx, y, z, t = symbols('x y z t')\nk, m, n, p, q = symbols('k m n p q', integer=True)\nf, g, h = symbols('f g h', cls=Function)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "\u041e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u044b\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "dsolve(f(x).diff(x)*(2*x+1)-4*x-2*f(x),f(x)) # 137",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": "$$f{\\left (x \\right )} = C_{1} + C_{2} x + 2 x \\log{\\left (2 x + 1 \\right )} + \\log{\\left (2 x + 1 \\right )}$$",
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAAYCAYAAADeW8faAAAABHNCSVQICAgIfAhkiAAACEBJREFU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\nHCarVUb9hQAAAABJRU5ErkJggg==\n",
       "prompt_number": 2,
       "text": "f(x) = C\u2081 + C\u2082\u22c5x + 2\u22c5x\u22c5log(2\u22c5x + 1) + log(2\u22c5x + 1)"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "dsolve(f(x).diff(x) + 2*f(x) - f(x)**2*exp(x), f(x)) # 151",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": "$$f{\\left (x \\right )} = \\frac{e^{- 2 x}}{C_{1} + e^{- x}}$$",
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGYAAAAoCAYAAAAMjY9+AAAABHNCSVQICAgIfAhkiAAABBZJREFU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\nsF3/S9qCgoKCgoKCgmz4HztCxVdUZUYYAAAAAElFTkSuQmCC\n",
       "prompt_number": 3,
       "text": "         -2\u22c5x  \n        \u212f      \nf(x) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n             -x\n       C\u2081 + \u212f  "
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "dsolve(f(x)/(3*x - f(x)**2)-f(x).diff(x), f(x)) # 149 ???",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": "$$f{\\left (x \\right )} = C_{1} e^{- \\int - \\frac{1}{3 x - f^{2}{\\left (x \\right )}}\\, dx}$$",
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKkAAAAwCAYAAABqvFqkAAAABHNCSVQICAgIfAhkiAAABsBJREFU\neJzt3HuMXFUdwPFPl+1KhVZoQUwrpg+oFm0LEsBlhdRifaCNSY2GqMWKxKYiCK3gAxU1EmOpkBgQ\nAa28kpqgIESMRIjKKgFNfYCaIvJIRcFXRFFBENY/fnc6d29ntjOzd+ZO6fkmk/s695zf3f3dc36P\nc+5eEv3Gm3EnhnB7xbIkEjsxDY9iJf6GvasVpz8YqFqAxDhOwiP4Jf6DsWrFSSR25jv4XNVCJBLN\nmIp/48SqBUkkmjEshvcDqhak30g2af8wgt/jr1UL0m8kJe0fhoXDlCiQlLR/OBa/qlqIfiQpaX8w\nFy/Cr3vY5gAu7GF7HTNYtQAJcEy2/U2P2nsB3otlPWov8RzgC3gWz+9xuz/ocXsdkYb7/uAoPCSy\nTIkCSUmrZwBH6K09WjUfEyPHS1opnJS0ehZiX3uWkn4D92F7K4WTklbPEdl2T1LSN+J7rRZO3n31\nvDLb3tPDNqdhLRZhPS7FE11sbxDniYzaEN6OjbnrIzgUS7EV++D1+BAe6KJciRa5BU/jeVUL0kW+\ngjOz/ZnieWdkxzNEOAzegruy/atE7Dj1pCVwOhZMcP0ubJng+mIRH/1vCXX1I0vEPNkDs+Ol4jn+\nmR0/hWuy/WHckO2/u1cCJiZmppj5dGWb94318a/Ienw3d/xZfBL7Nyi7VYTjiIQDkuNUNYuy7c/a\nvG9KH/+K/F2sNiBszVX4Pt6RnVuJs0RqeAl+kZ3f0ZM2qjTRO07FFXg1flyxLDVGhH18GC4uob69\ns3puy+o9WOjdVtyM9+BI3CscumdEUuN6/KmE9hOTZJNwItpNh04Xzsa7cLlyfYszsu0lJdY5KdJw\nXy2LcLf206HLsnuvFb3QK0qU6YviJfhLiXV2nUNEt7wRX7Z7KfbLhdyjuBXXieF1nhhydoQ5KuIB\nnQ2pA0KRhsSwWcbElNPERJfX4BTh1O0WDOF+IfTV+J/GXlm/MUMo43YxJOZjkAcKe+dr2NZ70Xaw\nr8hfr+7w/tk4F68tSZ6bxfqqc8RQvyl3bYp6XLNI5fqwUoQVFuBorKhWnJaYJ+KOd2BWkzIvE89V\nhmPQKa/KZDh0kvXcKl68/cTXTz6CNcIUaKZYRU7HjTiuyfVa6rZRG0uE1941dmVwLxMLw+7Pfv3O\nTBGTG8CbRPijEduEN3lbj+RqxGLxlZLfdXDvFPWY5J+Fcv0c38bhYh7ADVmZNQ3uf0Rkumr8MSs/\n2qS9/XPbYhvPiAD9HR08RymMig8W7C5sEf+YE1ooOyp6hqq4VJgdnbAR67L9H4n8/wzR6dwkXtKJ\nMldFzhc9YjNel20btTFHhKu6RrOe9CocJOJ320Tv9KAwrlcY/xYeiZPFGzVXxP7WCgWYIyYW7CU8\n2IfLfoAcx4j026jWesiL8ViLdR+O94ueeaqw3U7D4+2LuYNhbO7w3quFUq3FN0Uy4HzRKz+I5XhS\n66PfIhMvXblXPPNZDdp4Cj9p+wlKYr7olVblzr1NGPz5Mpeoe/xX4rdi5eOIcAw2ZNfWTNDWZpFp\naOe3rFDHZZm8Zed814ilxnNy584RkyE65SDxt1k4iTrK5KtVC9Apq8Q/fX7u3BmFMl8SoZAa16nP\nYjlYeIg152W57g4L9wl5X1xincMi2D6SO3e08IRf2GZds4Xttx8+qMLeJ8cbcJG6Y7Tb8Rn8Qz11\nOk19ulWNeYXjh8Ww04hZIgXWLZ7Av1os26pHfYtwTC4QL9xFeJ/WveY8h2X1zccfxMTfxCS5CT/M\nHc8W9mYzXip6smZxu0F8tBzRGvKo6Kl2xYDWQk9TRVz4sskIVWCzsGPPK7HO5zwThaCW4lu548eM\nt0eLLBdGdD4UMV99ZvV0zR2VK7Q/5Gww/iW6U4Sd9hFfp2vGOny9cG66CO6vV193M0s4fGWG3k7J\nfokSqM1zLP5BN+T2p4lQyOLs+Hr8NHd9QNisNY4XkYBucZyIMBTt5jwrxErFPKfiU+J55+bODwpz\np1ieCL2sa3A+0UNOEP+0olKdrP6J7LdmZU4SGZx7RMyuxsfVv8xBzNrp9tTAM4Vdutr4OQaz8Amc\nPcG9RSUlXsLbjZf7eBHF6GqWJVGnmdKcLfLCBwi7rMaQ6I1qed4LREZqDJ8WPeeTYinEjerxyoWi\nZ+rFZ2SOFcq6IJPtceHQXb6L9seEI/hQ7twgPi8iBtvF898tTINnS5Y70SZbRJB4T6JRT5roA/JD\n4ofV10IfJRbwJxKVk1fS1cI7XyIC2ElJE31BXkk3iSDzucIperoSiRKJxE68U8xIGhPx0w9UK04i\nkUgkEolEIpFIJBJt8n/A7Gq6C9vvdgAAAABJRU5ErkJggg==\n",
       "prompt_number": 4,
       "text": "            \u2320               \n            \u23ae     -1        \n           -\u23ae \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 dx\n            \u23ae        2      \n            \u23ae 3\u22c5x - f (x)   \n            \u2321               \nf(x) = C\u2081\u22c5\u212f                 "
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "dsolve(x * f(x).diff(x) + x**2 + x*f(x)-f(x), f(x)) # 301",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": "$$f{\\left (x \\right )} = x \\left(C_{1} e^{- x} - 1\\right)$$",
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJoAAAAZCAYAAADJ2zdhAAAABHNCSVQICAgIfAhkiAAABSZJREFU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\nC/wLGd0lR042j2UAAAAASUVORK5CYII=\n",
       "prompt_number": 5,
       "text": "         \u239b    -x    \u239e\nf(x) = x\u22c5\u239dC\u2081\u22c5\u212f   - 1\u23a0"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "dsolve(f(x)*sin(x) + f(x).diff(x)*cos(x) - 1, f(x)) # 366",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": "$$f{\\left (x \\right )} = \\frac{\\cos{\\left (x \\right )}}{\\tan^{2}{\\left (\\frac{x}{2} \\right )} - 1} \\left(C_{1} + C_{2} \\tan^{2}{\\left (\\frac{x}{2} \\right )} - 2 \\tan{\\left (\\frac{x}{2} \\right )}\\right)$$",
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAAlCAYAAAC+n7XmAAAABHNCSVQICAgIfAhkiAAADUFJREFU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\n",
       "prompt_number": 6,
       "text": "       \u239b           2\u239bx\u239e        \u239bx\u239e\u239e       \n       \u239cC\u2081 + C\u2082\u22c5tan \u239c\u2500\u239f - 2\u22c5tan\u239c\u2500\u239f\u239f\u22c5cos(x)\n       \u239d            \u239d2\u23a0        \u239d2\u23a0\u23a0       \nf(x) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n                      2\u239bx\u239e                \n                   tan \u239c\u2500\u239f - 1            \n                       \u239d2\u23a0                "
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "dsolve(x*(x+1)*(f(x).diff(x)-1)-f(x), f(x)) # 338",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": "$$f{\\left (x \\right )} = \\frac{x}{x + 1} \\left(C_{1} + x + \\log{\\left (x \\right )}\\right)$$",
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANQAAAAbCAYAAAAEYKF5AAAABHNCSVQICAgIfAhkiAAABtlJREFU\neJzt3HuMXFUdwPGPW2wLpZV2ga4Rql1bX2ipUiW04KOEh5qKYkyqVWjaan3Lq6lB1ErUGIQIFYjY\nKFtNREWJj/ggahRLiI8QRVEpiGykiTaiFFGk5bH+8bvD3Jm9O3Nv984Ms73fZDP3nnPmnN/c8zvn\n/M7vd+5SUVFRGk/JUWYRrsAfMAfvxuOdFKoLrMBiHItbMQun4QL8pUsyHIOzcQL24n7swScxihFs\nxt+7JE8veT02YRDbcFlvxekc03E31uFLeBRzeyrR5JmD9cn1Gfhlcr0dQyW1cQguatH+NvwVb8WM\nVN4RuAHX4o6SZOkXnoX/YktvxcjNR3Fw0S+twhiejZfhlJKF6gUzxUQBn8IHS65/mph8jsrIW4g/\n4hYxG2fxPPHMryxBliU4qIR6utX+qP4ZUIvwFfmsvCe4DP/oiDhPDm7FS5Prp5VU5yZsyEifh524\nS/tV/g68oQRZRsTM3yuKtj+qfwYUvAPnFfnCDny/M7L0jFU4V3T0I3hqkv7+Euqeizs1mnE1rhMr\nz8k56tmBw0qQZ0Q1oDrJdNwu1VcTLcfbMR8nitnyh7gH7xFm342pssfhLDwmHt4GbEwaeYawNafh\nIewq65dMgsOFCbsKHxID6SF8rYS63yL2QHub0o/HajFQfpKjniuFg6Lb5OnLu3sg1/F4H3YLnT1M\nOG92NpVbh9NxrzC5fyRM6GX4Kj6HAY06PBn93YfvYS0ub/cjhsWMemYq7U04tKnMVYmQxIx0J5YL\nT9rjOD/JW9uirS/itwX/XtnuB/SAH+DVGenXiGd5dnfFKbRCFOnLTrRP9gq1SgycI1Jpz0/KvjiV\nthH/UTfdF4tBskwMstcl6WkdLkN/XyMmyracKZRgOJXWbBZdjdmp++vVvWZH41L1zfdKvCBPw33K\nQfif7P3RXeJZZjkqOsmI/ApdpC870T7jB9ShuA/nZJS9QkysNX6nLm+N3fhyU1pah8vQ30E8LLH2\nBjIK1FiKfwtTj3ARNpf/NB5M3Z+AHyfX94q4zj+T+9vE0j1VmS88Pvdn5B0lXMJ5TN7FZQpVgCJ9\n2S1eKxQ2K4SwU8QRj0vu7zN+7zpD47amWYfL0N9/JW0spLVLc6mYAcaS+7liSU1zT+r6ucLm/OkE\n9T2gvDjPk5Eh8RuzeEC+YPgAPoD3Fmx7u1CuZhaIcMe+jLz1wstZo0hfdqL9LGrW0aMZeY8kn4uS\nej4u9vrHiEMIpwunQTpI3KzDZejvmJhE59F6QB2Lb6Xu92jcPzWzUjy4W1Jpw+onD2abeKO9TaM9\nnIfzcVNyPdaqYIepxSEGWsjxCzHbzhIr1US8S2ye08wWgd7zRDA4i4n2ZiPChBpt0WYW7fqy0+3X\n+FvyeWRGXs0U2518PoyP4O1isE3HSzSubq10eDL6+5g2OjgvKbCuKT29KT0Yl+BFyf0N+HUqf0DY\nqDVerr48T0UWGO/dq3GSeOitXPOn4MKmtA1CIcfsn/t7JOf3ivZl2e3XGNW4hxoUE9DHMspeL8yy\n2qJwgQgkt6Omw2Xq7z48s1WjJ4tObK7gLHHSAN6YlFktXJO/x82pshdptDnXKxhV7jNmCNNkzgT5\n5whz420a7fhBfFgEhCei0wOqaF+W3X6NXcJ0S7MmSX96Km2h2DO9KpX2ZnxX6O4rxOo0ZLzO1XS4\nLP2dIybLmRl5T7BJLG/NJuF0YboQ8ZxrxcbuEmHObBcu4q0aA5jP0d8evtn4hliFWrFDmA4TsRxf\nFzb/jUmdl2v/bDo9oIr0ZSfaP0M8kzGxIt2kUUFPEsd8rsZn8QX1laXG4cKBMNb0t0sMyho1HS5L\nf1fiN+1+4HX4ZrtCU4R2DoAiZteFuHjyIo2j0wOqU3Sr/QVir3SqCMISA3JYmHh7xaDoBBeb4HTH\nZhFZhj+LJfRAYEvOcnmUeoEwHVqFI/aH/R1QW/XWs9qt9s/Ft1vk3yZMvLIZEP19dFbm7eIYxRL8\nSf2MW7+wQkSzPyNei9goNprDLb5DuQOKcNOuzllnXvZ3QB0ovFA4KJZn5J0qPHXzO9DuaqFvmazF\n58WZtn7b70zmHactOdvIq9SH4Ds52i1CNaDaMyz2VyPJ51Vij/QJsV8qmyNFP89KJ04Vr9tMETjd\nJ95x2pN8NjNfeNvSv/tEjd6dB0UnNDMmvEujOeQZEl6iogHaZtYk8r1TTHQ3K+c9qYrJs1Uc0J3y\nb1QXfcdpS856q1Wioi1lb557RfodpyXqhya7fbq74gBnWvsifcEKcYZrED8X58eWijhPq6M+xGsg\nP2uRv0b8Y5plIrg4hF9NStqKiinM5l4LUFFRUVFRUVFRUVHRN/wfnZ6epC1qQN0AAAAASUVORK5C\nYII=\n",
       "prompt_number": 7,
       "text": "       x\u22c5(C\u2081 + x + log(x))\nf(x) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n              x + 1       "
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}